Department of Mathematics
University of California, Santa Barbara
Math 6B
Vector Calculus II
| Text | Infinite Sequence Introduction |
| Text | Infinite Series Introduction | See next few lectures for definitions of con/divergence, geometric series |
| Video - 0:11:26 | Convergence and Divergence of Sequences |
| Video - 0:06:21 | Examples of Converging and Diverging Sequences |
| Video - 0:12:24 | Convergence and Divergence of Series, Geometric Series, Divergence Test |
| Text | Summary of Convergence Tests | See earlier lectures for descriptions of each test |
| Video - 0:08:20 | Integral Test Example |
| Video - 0:07:35 | Comparisson and Limit Comparisson Test examples | See next video as well |
| Video - 0:06:01 | Alternating Series Test examples | See next two videos as well |
| Video - 0:07:38 | Ratio Test examples | See next video as well |
| Video - 0:11:21 | Examples using absolute and conditional convergence |
| Video - 0:12:47 | Looking at which tests work for which examples |
| Text | Introduction to Power Series and Interval of Convergence |
| Text | Taylor Series Examples |
| Video - 0:09:47 | Examples of finding Intervals of Convergence |
| Video - 0:06:30 | Maclaurin Series Example | See next video for Taylor Series example |
| Interactive | Visualize a Taylor series approximating a function |
| Text | First of five lectures on Fourier series | See next four lectures as well for a more complete summary of Fourier series |
| Interactive | Calculates first several terms in a Fourier series |
| Various | Self-contained class material on Fourier series |
| Text | Introduction to separation of variables for PDEs | The lectures which follow offer a nice summary of how to use separation of variables to solve basic heat, wave, and Laplace equations |
